Over the past several decades, significant efforts have been directed toward solving constrained multiple objective optimization (MOO) problems. Meanwhile, MOO problem formulations have found their practical applications in many engineering areas; for example, engineering applications, energy and power grids, VLSI design, finance, vehicle routing problems, and machine learning, to name a few.
Many MOO methods, such as population-based meta-heuristics, including NSGA-II [1], MOEA/D [2], the deterministic method [3], MOEA-DLA [4], and cultural MOPSO [5], have been proposed to solve MOO problems with the focus of computing the entire Pareto front. However, from application perspectives, MOO decision makers (users) may not always be interested in knowing the entire Pareto front of a MOO problem. Instead, they may have their own wish list regarding the range of each objective function.
The following publications describe some of the existing MOO methods, which are incorporated herein by reference.    [1] K. Deb, A. Pratap, S. Agarwal, and T. Meyarivan, “A fast and elitist multi-objective genetic algorithm: NSGA-II,” IEEE Trans. on Evolutionary Computation, vol. 6, no. 2, pp. 182-197, April 2002.    [2] K. Li, S. Kwong, Q. Zhang and K. Deb, “Interrelationship-Based Selection for Decomposition Multiobjective Optimization,” in IEEE Trans. on Cybernetics, vol. 45, no. 10, pp. 2076-2088, October 2015.    [3] X. B. Hu, M. Wang and E. Di Paolo, “Calculating Complete and Exact Pareto Front for Multiobjective Optimization: A New Deterministic Approach for Discrete Problems,” in IEEE Trans. on Cybernetics, vol. 43, no. 3, pp. 1088-1101, June 2013.    [4] N. Chen et al., “An Evolutionary Algorithm with Double-Level Archives for Multiobjective Optimization,” in IEEE Trans. on Cybernetics, vol. 45, no. 9, pp. 1851-1863, September 2015.    [5] M. Daneshyari and G. G. Yen, “Cultural-Based Multiobjective Particle Swarm Optimization,” in IEEE Trans. on Systems, Man, and Cybernetics, Part B (Cybernetics), vol. 41, no. 2, pp. 553-567, April 2011.